In this work, we directly fit the QCD dimensional transmutation parameter, [Formula: see text], to experimental data of Drell–Yan (DY) observables. For this purpose, we first obtain the evolution of transverse momentum dependent parton distribution functions (TMDPDFs) up to the next-to-next-to-leading logarithm (NNLL) approximation based on Collins–Soper–Sterman (CSS) formalism. As is expecting the TMDPDFs are appearing at larger values of transverse momentum by increasing the energy scales and also the order of approximation. Then we calculate the cross-section related to the TMDPDFs in the DY process. As a consequence of global fitting to the five sets of experimental data at different low center-of-mass energies and one set at high center-of-mass energy, using CETQ06 parametrizations as our boundary condition, we obtain [Formula: see text] MeV corresponding to the renormalized coupling constant [Formula: see text] which is within the acceptable range for this quantity. The goodness of [Formula: see text] shows the results for DY cross-section are in good agreement with different experimental sets, containing E288, E605 and R209 at low center-of-mass energies and [Formula: see text], CDF data at high center-of-mass energy. The repeated calculations, using HERAPDFs parametrizations is yielding us numerical values for fitted parameters very close to what we obtain using CETQ06 PDFs set. This indicates that the obtained results have enough stability by variations in the boundary conditions.
Measurement of the transverse momentum differential cross-section for Z boson decays to muon anti-muon events in proton anti-proton collisions at center-of-mass energy = 1.8-TeV
